Solve by the method of substitution.
Answers
Answer:
this is the answer
Question:
Solve by the method of substitution.
( 5 / x ) + 3y = 8
( 4 / x ) + 10y = 56
Answer:
The solution of the given equations is
( x, y ) = ( - 19 / 44, 124 / 19 ).
Step-by-step-explanation:
The given linear equations are
( 5 / x ) + 3y = 8
⇒ ( 5 + 3xy ) / x = 8
⇒ 5 + 3xy = 8x
⇒ 3xy = 8x - 5
⇒ y = ( 8x - 5 ) / 3x - - - ( 1 ) &
( 4 / x ) + 10y = 56
⇒ ( 4 + 10xy ) / x = 56
⇒ 10xy + 4 = 56x
⇒ [ 10x ( 8x - 5 ) / 3x ] + 4 = 56x - - - [ From ( 1 ) ]
⇒ [ ( 80x² - 50x ) / 3x ] + 4 = 56x
⇒ ( 80x² - 50x + 12x ) / 3x = 56x
⇒ 80x² - 38x = 56x * 3x
⇒ 80x² - 38x = 168x²
⇒ 80x² - 38x - 168x² = 0
⇒ - 88x² - 38x = 0
⇒ - 2x ( 44x + 19 ) = 0
⇒ - 2x = 0 OR ( 44x + 19 ) = 0
⇒ x = - 0 / 2 OR 44x + 19 = 0
⇒ x = 0 OR 44x = - 19
⇒ x = 0 OR x = - 19 / 44
As x is in denominator in both equations,
∴ x = 0 is unacceptable.
x = - 19 / 44
Now,
y = ( 8x - 5 ) / 3x - - - ( 1 )
⇒ y = [ ( 8 * - 19 / 44 ) - 5 ] / 3 * ( - 19 / 44 )
⇒ y = [ ( 2 * - 19 / 11 ) - 5 ] / ( - 57 / 44 )
⇒ y = [ ( - 38 / 11 ) - 5 ] / ( - 57 / 44 )
⇒ y = [ ( - 38 - 55 ) / 11 ] / ( - 57 / 44 )
⇒ y = ( - 93 / 11 ) / ( - 57 / 44 )
⇒ y = ( - 93 / 11 ) * ( - 44 / 57 )
⇒ y = ( - 93 * - 44 ) / ( 11 * 57 )
⇒ y = ( 93 / 57 ) * ( 44 / 11 )
⇒ y = ( 31 / 19 ) * 4
⇒ y = 124 / 19
∴ The solution of the given equations is
( x, y ) = ( - 19 / 44, 124 / 19 ).